A homogenous cylinder with radius R and mass M is resting, with the axis vertical, on a horizontal surface, which can be asumed to be completely slippery. A string is partially wound around the cylinder. The string then runs over a pulley at the end of the table, in the same height as the winding, and then on to a weight with mass m hanging in its other end. Determine the angular acceleration and the tension in the string when the system is moving. The moment of intertia of the pulley can be neglected.
F = ma
RF = Iα
The Attempt at a Solution
I'm going crazy with this, because it's not really that hard of a problem..
Okay, if I draw the force diagrams, I have the tension T on the cylinder, which is the force that will create its angular acceleration and I have T up and mg down on the mass m. The tension should also be the force that's accelerating the centre of mass of M. I'd say the translational acceleration of M needs to be the same as that for m.
m: mg - T = ma
M: T = Ma
rotation: RT = Iα
I for a cyldinder = MR2/2
from rotation: T = MRα/2
from M: a = T/M
a = Rα/2
Putting these in the m-equation: mg - MRα/2 = mRα/2
mg = Rα(M + m)/2
2mg/R(M + m) = α
And this is incorrect. There's something I'm missing and I can't see it - it is driving me insane. The correct answer is supposed to be α = 2mg/R(M + 3m). So close, yet sooo far away.
Could anyone tell me what I'm not seeing, please?